Question

And wins a metal in the shape of a circle for finishing a marathon which statements about the metals are true use 3.14 for pi. Select all that are correct A. If the Metal has a circumference of seven pi inches Then it has a diameter Of 3.5in. B. If the metal has a circumference of three pi inches then it has an area of nine pi square inches. C. If the metal has a radius of 2.5 inches then it has an area of 19.625 in.² D. If the metal has a diameter of 3 inches and it has a circumference of 9.42 inches. E. If the metal has a circumference of four pi inches then it has an area of four pi square inches

Answer 1

Answer:

The true statements are:

C. If the metal has a radius of 2.5 inches then it has an area of 19.625 in.²

D. If the metal has a diameter of 3 inches and it has a circumference of 9.42 inches.

E. If the metal has a circumference of four pi inches then it has an area of four pi square inches

Step-by-step explanation:

Let us revise the rule of circumference and area of a circle

• The formula of the circumference of a circle is C = π d, where d is the diameter of the circle OR C = 2πr, where r is the radius of the circle
• The formula of the area of a circle is A = πr²
• The radius of a circle is equal to half its diameter

A.

∵ The metal has a circumference of 7π inches

∵ C = 2πr

- Equate πd by 7π

∴ πd = 7π

- Divide both sides by π

∴ d = 7 inches not 3.5 inches

∴ A is not true

B.

∵ The metal has a circumference of 3π inches

∵ C = 2πr

- Equate 2πr by 3π

∴ 2πr = 3π

- Divide both sides by π

∴ 2r = 3

- Divide both sides by 2

∴ r = 1.5 inches

∵ A = πr²

∴ A = π(1.5)²

∴ A = 2.25π inches² not 9π inches²

∴ B is not true

C.

∵ The metal has a radius of 2.5 inches

∴ r = 2.5

∵ A = πr²

∵ π = 3.14

∴ A = 3.14(2.5)²

∴ A = 19.625 inches²

∴ If the metal has a radius of 2.5 inches, then its area is 19.625 in.²

∴ C is true

D.

∵ The metal has a diameter of 3 inches

∴ d = 3

∵ C = πd

∵ π = 3.14

∴ C = 3.14(3)

∴ C = 9.42 inches

∴ If the metal has a diameter of 3 inches, then its circumference

  is 9.42 inches

∴ D is true

E.

∵ The metal has a circumference of 4π inches

∵ C = 2πr

- Equate 2πr by 4π

∴ 2πr = 4π

- Divide both sides by 2π

∴ r = 2

- Now you can find the area

∵ A = πr²

∴ A = π(2)²

∴ A = 4π

∴ If the metal has a circumference of 4π inches, then its area

   is 4π  inches²

∴ E is true

The true statements are:

C. If the metal has a radius of 2.5 inches then it has an area of 19.625 in.²

D. If the metal has a diameter of 3 inches and it has a circumference of 9.42 inches.

E. If the metal has a circumference of four pi inches then it has an area of four pi square inches